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<li><a class="reference internal" href="#">Comparison of Calibration of Classifiers</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-calibration-plot-compare-calibration-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
</div>
<div class="sphx-glr-example-title section" id="comparison-of-calibration-of-classifiers">
<span id="sphx-glr-auto-examples-calibration-plot-compare-calibration-py"></span><h1>Comparison of Calibration of Classifiers<a class="headerlink" href="#comparison-of-calibration-of-classifiers" title="Permalink to this headline">¶</a></h1>
<p>Well calibrated classifiers are probabilistic classifiers for which the output
of the predict_proba method can be directly interpreted as a confidence level.
For instance a well calibrated (binary) classifier should classify the samples
such that among the samples to which it gave a predict_proba value close to
0.8, approx. 80% actually belong to the positive class.</p>
<p>LogisticRegression returns well calibrated predictions as it directly
optimizes log-loss. In contrast, the other methods return biased probabilities,
with different biases per method:</p>
<ul class="simple">
<li><p>GaussianNaiveBayes tends to push probabilities to 0 or 1 (note the counts in
the histograms). This is mainly because it makes the assumption that features
are conditionally independent given the class, which is not the case in this
dataset which contains 2 redundant features.</p></li>
<li><p>RandomForestClassifier shows the opposite behavior: the histograms show
peaks at approx. 0.2 and 0.9 probability, while probabilities close to 0 or 1
are very rare. An explanation for this is given by Niculescu-Mizil and Caruana
<a class="footnote-reference brackets" href="#id3" id="id1">1</a>: “Methods such as bagging and random forests that average predictions
from a base set of models can have difficulty making predictions near 0 and 1
because variance in the underlying base models will bias predictions that
should be near zero or one away from these values. Because predictions are
restricted to the interval [0,1], errors caused by variance tend to be one-
sided near zero and one. For example, if a model should predict p = 0 for a
case, the only way bagging can achieve this is if all bagged trees predict
zero. If we add noise to the trees that bagging is averaging over, this noise
will cause some trees to predict values larger than 0 for this case, thus
moving the average prediction of the bagged ensemble away from 0. We observe
this effect most strongly with random forests because the base-level trees
trained with random forests have relatively high variance due to feature
subsetting.” As a result, the calibration curve shows a characteristic
sigmoid shape, indicating that the classifier could trust its “intuition”
more and return probabilities closer to 0 or 1 typically.</p></li>
<li><p>Support Vector Classification (SVC) shows an even more sigmoid curve as
the  RandomForestClassifier, which is typical for maximum-margin methods
(compare Niculescu-Mizil and Caruana <a class="footnote-reference brackets" href="#id3" id="id2">1</a>), which focus on hard samples
that are close to the decision boundary (the support vectors).</p></li>
</ul>
<div class="topic">
<p class="topic-title">References:</p>
<dl class="footnote brackets">
<dt class="label" id="id3"><span class="brackets">1</span><span class="fn-backref">(<a href="#id1">1</a>,<a href="#id2">2</a>)</span></dt>
<dd><p>Predicting Good Probabilities with Supervised Learning,
A. Niculescu-Mizil &amp; R. Caruana, ICML 2005</p>
</dd>
</dl>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>

<span class="c1"># Author: Jan Hendrik Metzen &lt;jhm@informatik.uni-bremen.de&gt;</span>
<span class="c1"># License: BSD Style.</span>

<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>

<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>

<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
<span class="kn">from</span> <span class="nn">sklearn.naive_bayes</span> <span class="kn">import</span> <span class="n">GaussianNB</span>
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">RandomForestClassifier</span>
<span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">LinearSVC</span>
<span class="kn">from</span> <span class="nn">sklearn.calibration</span> <span class="kn">import</span> <span class="n">calibration_curve</span>

<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">make_classification</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">100000</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span>
                                    <span class="n">n_informative</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">n_redundant</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>

<span class="n">train_samples</span> <span class="o">=</span> <span class="mi">100</span>  <span class="c1"># Samples used for training the models</span>

<span class="n">X_train</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:</span><span class="n">train_samples</span><span class="p">]</span>
<span class="n">X_test</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">train_samples</span><span class="p">:]</span>
<span class="n">y_train</span> <span class="o">=</span> <span class="n">y</span><span class="p">[:</span><span class="n">train_samples</span><span class="p">]</span>
<span class="n">y_test</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">train_samples</span><span class="p">:]</span>

<span class="c1"># Create classifiers</span>
<span class="n">lr</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">()</span>
<span class="n">gnb</span> <span class="o">=</span> <span class="n">GaussianNB</span><span class="p">()</span>
<span class="n">svc</span> <span class="o">=</span> <span class="n">LinearSVC</span><span class="p">(</span><span class="n">C</span><span class="o">=</span><span class="mf">1.0</span><span class="p">)</span>
<span class="n">rfc</span> <span class="o">=</span> <span class="n">RandomForestClassifier</span><span class="p">()</span>


<span class="c1"># #############################################################################</span>
<span class="c1"># Plot calibration plots</span>

<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">ax1</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot2grid</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">rowspan</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">ax2</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot2grid</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>

<span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">&quot;k:&quot;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Perfectly calibrated&quot;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">clf</span><span class="p">,</span> <span class="n">name</span> <span class="ow">in</span> <span class="p">[(</span><span class="n">lr</span><span class="p">,</span> <span class="s1">&#39;Logistic&#39;</span><span class="p">),</span>
                  <span class="p">(</span><span class="n">gnb</span><span class="p">,</span> <span class="s1">&#39;Naive Bayes&#39;</span><span class="p">),</span>
                  <span class="p">(</span><span class="n">svc</span><span class="p">,</span> <span class="s1">&#39;Support Vector Classification&#39;</span><span class="p">),</span>
                  <span class="p">(</span><span class="n">rfc</span><span class="p">,</span> <span class="s1">&#39;Random Forest&#39;</span><span class="p">)]:</span>
    <span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
    <span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="s2">&quot;predict_proba&quot;</span><span class="p">):</span>
        <span class="n">prob_pos</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">]</span>
    <span class="k">else</span><span class="p">:</span>  <span class="c1"># use decision function</span>
        <span class="n">prob_pos</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">decision_function</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
        <span class="n">prob_pos</span> <span class="o">=</span> \
            <span class="p">(</span><span class="n">prob_pos</span> <span class="o">-</span> <span class="n">prob_pos</span><span class="o">.</span><span class="n">min</span><span class="p">())</span> <span class="o">/</span> <span class="p">(</span><span class="n">prob_pos</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">-</span> <span class="n">prob_pos</span><span class="o">.</span><span class="n">min</span><span class="p">())</span>
    <span class="n">fraction_of_positives</span><span class="p">,</span> <span class="n">mean_predicted_value</span> <span class="o">=</span> \
        <span class="n">calibration_curve</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">prob_pos</span><span class="p">,</span> <span class="n">n_bins</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>

    <span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">mean_predicted_value</span><span class="p">,</span> <span class="n">fraction_of_positives</span><span class="p">,</span> <span class="s2">&quot;s-&quot;</span><span class="p">,</span>
             <span class="n">label</span><span class="o">=</span><span class="s2">&quot;</span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="p">))</span>

    <span class="n">ax2</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">prob_pos</span><span class="p">,</span> <span class="nb">range</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">bins</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">name</span><span class="p">,</span>
             <span class="n">histtype</span><span class="o">=</span><span class="s2">&quot;step&quot;</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>

<span class="n">ax1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Fraction of positives&quot;</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">])</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">&quot;lower right&quot;</span><span class="p">)</span>
<span class="n">ax1</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">&#39;Calibration plots  (reliability curve)&#39;</span><span class="p">)</span>

<span class="n">ax2</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Mean predicted value&quot;</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Count&quot;</span><span class="p">)</span>
<span class="n">ax2</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">&quot;upper center&quot;</span><span class="p">,</span> <span class="n">ncol</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
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